1,291 research outputs found
Fork-decompositions of matroids
For the abstract of this paper, please see the PDF file
On matroids of branch-width three
For the abstract of this paper, please see the PDF file
Improved alkaline electrochemical cell
Addition of lead ions to electrolyte suppresses zinc dendrite formation during charging cycle. A soluble lead salt can be added directly or metallic lead can be incorporated in the zinc electrode and allowed to dissolve into the electrolyte
The structure of the 3-separations of 3-connected matroids II
The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid. The purpose of this paper is to show that if certain natural conditions are imposed on the tree, then it has a uniqueness property. In particular; suppose that, from every pair of edges that meet at a degree-2 vertex and have their other ends of degree at least three, one edge is contracted. Then the resulting tree is unique
The structure of the 3-separations of 3-connected matroids
Special Issue Dedicated to Professor W.T. TutteTutte defined a k-separation of a matroid M to be a
partition (A,B) of the ground set of M such that ∣A∣,∣B∣ ≥ k and
r(A) + r(B) − r(M) < k. If, for all m < n, the matroid M has no
m-separations, then M is n-connected. Earlier, Whitney showed that
(A,B) is a 1-separation of M if and only if A is a union of 2-connected
components of M. When M is 2-connected, Cunningham and Edmonds
gave a tree decomposition of M that displays all of its 2-separations.
When M is 3-connected, this paper describes a tree decomposition of
M that displays, up to a certain natural equivalence, all non-trivial 3-separations of M
On the matroids in which all hyperplanes are binary
In this paper, it is shown that, for a minor-closed class ℳ of matroids, the class of matroids in which every hyperplane is in ℳ is itself minor-closed and has, as its excluded minors, the matroids U1,1 ⊕ N such that N is an excluded minor for ℳ. This result is applied to the class of matroids of the title, and several alternative characterizations of the last class are given
On Local Equivalence, Surface Code States and Matroids
Recently, Ji et al disproved the LU-LC conjecture and showed that the local
unitary and local Clifford equivalence classes of the stabilizer states are not
always the same. Despite the fact this settles the LU-LC conjecture, a
sufficient condition for stabilizer states that violate the LU-LC conjecture is
missing. In this paper, we investigate further the properties of stabilizer
states with respect to local equivalence. Our first result shows that there
exist infinitely many stabilizer states which violate the LU-LC conjecture. In
particular, we show that for all numbers of qubits , there exist
distance two stabilizer states which are counterexamples to the LU-LC
conjecture. We prove that for all odd , there exist stabilizer
states with distance greater than two which are LU equivalent but not LC
equivalent. Two important classes of stabilizer states that are of great
interest in quantum computation are the cluster states and stabilizer states of
the surface codes. To date, the status of these states with respect to the
LU-LC conjecture was not studied. We show that, under some minimal
restrictions, both these classes of states preclude any counterexamples. In
this context, we also show that the associated surface codes do not have any
encoded non-Clifford transversal gates. We characterize the CSS surface code
states in terms of a class of minor closed binary matroids. In addition to
making connection with an important open problem in binary matroid theory, this
characterization does in some cases provide an efficient test for CSS states
that are not counterexamples.Comment: LaTeX, 13 pages; Revised introduction, minor changes and corrections
mainly in section V
Feynman graph polynomials
The integrand of any multi-loop integral is characterised after Feynman
parametrisation by two polynomials. In this review we summarise the properties
of these polynomials. Topics covered in this article include among others:
Spanning trees and spanning forests, the all-minors matrix-tree theorem,
recursion relations due to contraction and deletion of edges, Dodgson's
identity and matroids.Comment: 35 pages, references adde
Fabrication of integrated planar gunn diode and micro-cooler on GaAs substrate
We demonstrate fabrication of an integrated
micro cooler with the planar Gunn diode and characterise
its performance. First experimental results have shown a
small cooling at the surface of the micro cooler. This is first
demonstration of an integrated micro-cooler with a planar
Gunn diode
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